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Journal of Systems Engineering and Electronics 2009年第2期20卷 321-326页

作者： Wang Jianqiang Zhang Zhong School of Business Central South Univ. Changsha 410083 P. R. China

Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are proposed. Expected values, score function, and accuracy function of intuitionitsic trapezoidal fuzzy numbers are defined. Based on these, a kind of intuitionistic trapezoidal fuzzy multi-criteria decision making method is proposed. By using these aggregation operators, criteria values are aggregated and integrated intuitionistic trapezoidal fuzzy numbers of alternatives are attained. By comparing score function and accuracy function values of integrated fuzzy numbers, a ranking of the whole alternative set can be attained. An example is given to show the feasibility and availability of the method.

关键词： intuitionistic trapezoidal fuzzy numbers aggregation operators multi-criteria decision making

Hierarchical medical diagnosis approach for COVID-19 based on picture fuzzy fairly aggregation operators

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International Journal of Biomathematics 2023年第2期16卷 115-151页

作者： Muhammad Riaz Hafiz Muhammad Athar Faridt Department of Mathematics University of the Punjab LahorePakistan

In Pakistan, a hierarchical healthcare system is an efficient way of addressing the issueof limited and insufficient healthcare services. Identifying the various degrees of diseasebased on the doctor's diagnosis is an important step in developing the hierarchical healthcaretreatment structure. This research presents a framework for dealing with the issueof diagnosis values presented as "picture fuzzy numbers (PFNs)". Specifically, the goal ofthis study is to establish some innovative operational laws and "aggregation operators"(AOs) in a picture fuzzy environment. In this regard, we proposed some new neutral orfair operational laws that incorporate the concept of proportional distribution in orderto achieve a neutral or fair remedy to the positive, neutral and negative aspects ofPFNs. Based on the developed operational laws, we proposed the "picture fuzzy fairlyweighted average operator" and the "picture fuzzy fairly ordered weighted averagingoperator". Compared to previous techniques, the proposed AOs provide more generalizedand reliable. Furthermore, using proposed AOs with multiple decision-makers andpartial weight information under PFNs, a "multi-criteria decision-making" algorithmis developed. Finally, we provide an example to show how the novel approach can aidhierarchical treatment systems. This is essential for merging the healthcare capabilitiesof the general public and optimizing the medical care system's service performance.

关键词： Fairly operations picture fuzzy numbers hierarchical healthcare treatment COVID-19 optimization model aggregation operators

Aczel-Alsina Weighted aggregation operators of Simplified Neutrosophic Numbers and Its Application in Multiple Attribute Decision Making

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Computer Modeling in Engineering & Sciences 2022年第8期132卷 569-584页

作者： Rui Yong Jun Ye Shigui Du Aqin Zhu Yingying Zhang Rock Mechanics Institute Ningbo UniversityNingbo315211China School of Civil and Environmental Engineering Ningbo UniversityNingbo315211China

The simplified neutrosophic number(SNN)can represent uncertain,imprecise,incomplete,and inconsistent information that exists in scientific,technological,and engineering fields.Hence,it is a useful tool for describing truth,falsity,and indeterminacy information in multiple attribute decision-making(MADM)problems.To suit decision makers’preference selection,the operational flexibility of aggregation operators shows its importance in dealing with the flexible decision-making problems in the SNN environment.To solve this problem,this paper develops the Aczel-Alsina aggregation operators of SNNs for MADM problems in view of the Aczel-Alsina operational flexibility.First,we define the Aczel-Alsina operations of SNNs.Then,the Aczel-Alsina aggregation operators of SNNs are presented based on the defined Aczel-Alsina operations of SNNs.Next,a MADM method is established using the proposed aggregation operators under the SNN environment.Lastly,an illustrative example about slope treatment scheme choices is provided to indicate the practicality and efficiency of the established method.By comparison with the existing relative MADM methods,the results show that the established MADM method can overcome the insufficiency of decision flexibility in the existing MADM methods and demonstrate the metric of flexible decision-making.

关键词： Simplified neutrosophic number multiple attribute decision-making aggregation operators

Novel Decision Making Methodology under Pythagorean Probabilistic Hesitant Fuzzy Einstein aggregation Information

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Computer Modeling in Engineering & Sciences 2023年第8期136卷 1785-1811页

作者： Shahzaib Ashraf Bushra Batool Muhammad Naeem Institute of Mathematics Khwaja Fareed University of Engineering&Information TechnologyRahim Yar Khan64200Pakistan Department of Mathematics University of SargodhaSargodha40100Pakistan Department of Mathematics Deanship of Applied SciencesUmm Al-Qura UniversityMakkah24382Saudi Arabia

This research proposes multicriteria decision-making(MCDM)-based real-time Mesenchymal stem cells(MSC)transfusion framework.The testing phase of the methodology denotes the ability to stick to plastic surfaces,the upregulation and downregulation of certain surface protein markers,and lastly,the ability to differentiate into various cell types.First,two scenarios of an enhanced dataset based on a medical perspective were created in the development phase to produce varying levels of emergency.Second,for real-timemonitoring ofCOVID-19 patients with different emergency levels(i.e.,mild,moderate,severe,and critical),an automated triage algorithmbased on a formal medical guideline is proposed,taking into account the improvement and deterioration procedures fromone level to the next.For this strategy,Einstein aggregation information under the Pythagorean probabilistic hesitant fuzzy environment(PyPHFE)is developed.Einstein operations on PyPHFE such as Einstein sum,product,scalar multiplication,and their properties are investigated.Then,several Pythagorean probabilistic hesitant fuzzy Einstein aggregation operators,namely the Pythagorean probabilistic hesitant fuzzy weighted average(PyPHFWA)operator,Pythagorean probabilistic hesitant fuzzy Einstein weighted geometric(PyPHFEWG)operator,Pythagorean probabilistic hesitant fuzzy Einstein ordered weighted average(PyPHFEOWA)operator,Pythagorean probabilistic hesitant fuzzy Einstein ordered weighted geometric(PyPHFEOWG)operator,Pythagorean probabilistic hesitant fuzzy Einstein hybrid average(PyPHFEHA)operator and Pythagorean probabilistic hesitant fuzzy Einstein hybrid geometric(PyPHFEHG)operator are investigated.All the above-mentioned operators are helpful in design the algorithm to tackle uncertainty in decision making problems.In last,a numerical case study of decision making is presented to demonstrate the applicability and validity of the proposed technique.Besides,the comparison of the existing and the proposed technique is established to show the effectiveness and valid

关键词： Pythagorean probabilistic hesitant fuzzy set aggregation operators decision making

aggregation operators and Distance Measures for Probabilistic q-Rung Orthopair Hesitant Fuzzy Sets and Their Applications

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Aggregation Operators and Distance Measures for Probabilisti...

Multiplicative Integral Theory of Generalized Orthopair Fuzzy Sets and Its Applications

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作者： Wenjing Yin Tingting Zheng Longmei Li School of Mathematical Sciences Anhui University

A q-rung orthopair fuzzy set（q-ROFS） is an effective tool for describing uncertainty and fuzziness, and is the promotion of intuitionistic fuzzy sets（IFSs） and Pythagorean fuzzy sets（PFSs）. This paper extends q-rung orthopair fuzzy environment to probabilistic q-rung orthopair hesitant fuzzy environment, and proposes the concept of probabilistic q-rung orthopair hesitant fuzzy sets（P-q-ROHFSs）. Some desired operational laws and properties of P-q-ROHFSs are studied. And we develop the some aggregation operators for probabilistic q-rung orthopair hesitant fuzzy information. Then the relationship among these operators is discussed by comparing the score function. In order to measure the uncertain information, this paper proposes the four distance measures between two P-q-ROHFSs. Especially, ranking and expansion of P-q-ROHFSs are discussed in detail. Furthermore,we apply them to pattern recognition and multi-attribute group decision making（MAGDM） under probabilistic q-rung orthopair hesitant fuzzy environment. Finally, examples are given to show the rationality and practicability of the proposed method.

关键词： Probabilistic q-rung orthopair hesitant fuzzy set（P-q-ROHFS） Distance measure aggregation operators Pattern recognition Multi-attribute group decision making（MAGDM）

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Journal of Systems Science and Systems Engineering 2022年第4期31卷 457-479页

作者： Jie Gao Zeshui Xu Chao Zhong Yunshu Mao School of Business Administration Southwestern University of Finance and EconomicsChengdu610207China Business School Sichuan UniversityChengdu610064China

There are two main issues of fuzzy multi-attribute decision-making:determine the weight of each attribute and choose an appropriate aggregation method to integrate the evaluation information of different attributes.In order to solve the multi-attribute decision-making problem in generalized orthopair fuzzy environment with unknown attribute weights more effectively,we give a decision-making method based on generalized orthopair fuzzy definite integrals.To be specific,we first introduce the complement operations of q-rung orthopair fuzzy numbers,and then investigate the multiplicative q-rung orthopair fuzzy calculus.Through the complement operations,we establish the mutual conversion formula between additive and multiplicative q-rung orthopair fuzzy calculus theory.Then,we give a multiplicative integral-based q-rung orthopair fuzzy multi-attribute decision-making method,and discuss the relationship between the q-rung orthopair fuzzy definite integrals and the q-rung orthopair fuzzy weighted geometric operator.Compared with traditional decision-making methods,this method does not rely on subjective weight information,which is especially important when dealing with large sample data.Finally,the application of election is studied to verify the feasibility and effectiveness of the proposed method.With the introduction of generalized orthopair fuzzy sets,the expression form of election evaluation information has been expanded.We also provide some examples to compare the obtained results with the results generated by the addition operation and reveal the correlation between them.

关键词： Fuzzy sets decision making aggregation operators

Analysis of TOPSIS techniques based on bipolar complex fuzzy N-soft setting and their applications in decision-making problems

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CAAI Transactions on Intelligence Technology 2023年第2期8卷 478-499页

作者： Tahir Mahmood Ubaid ur Rehman Zeeshan Ali Izatmand Haleemzai Department of Mathematics and Statistics International Islamic University IslamabadIslamabadPakistan Department of Higher Mathematics Polytechnical University KabulKabulAfghanistan

A novel model termed a bipolar complex fuzzy N-soft set(BCFN-SS)is initiated for tackling information that involves positive and negative aspects,the second dimension,and parameterised grading simultaneously.The theory of BCFN-SS is the generalisation of two various theories,that is,bipolar complex fuzzy(BCF)and N-SS.The invented model of BCFN-SS helps decision-makers to cope with the genuine-life dilemmas containing BCF information along with parameterised grading at the same time.Further,various algebraic operations,including the usual type of union,intersection,complements,and a few others types,are invented.Certain primary operational laws for BCFNSS are also invented.Moreover,a technique for order preference by similarity to the ideal solution(TOPSIS)approach is devised in the setting of BCFN-SS for managing strategic decision-making(DM)dilemmas containing BCFN-SS information.Keeping in mind the usefulness and benefits of the TOPSIS approach,two various types of TOPSIS approaches in the environment of BCFN-SS are devised and then a numerical example for exposing the usefulness of the devised TOPSIS approach is interpreted.To disclose the prominence and benefits of the devised work,the devised approaches with numerous prevailing work are compared.

关键词： aggregation operators bipolar complex fuzzy N-soft sets decision-making similarity measures TOPSIS techniques

Multi-attribute Group Decision-making Based on Hesitant Bipolar-valued Fuzzy Information and Social Network

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Computer Systems Science & Engineering 2023年第3期44卷 1939-1950页

作者： Dhanalakshmi R Sovan Samanta Arun Kumar Sivaraman Jeong Gon Lee Balasundaram A Sanamdikar Sanjay Tanaji Priya Ravindran Department of Computer Science and Engineering KCG College of TechnologyChennai600097Tamil NaduIndia Department of Mathematics Tamralipta MahavidyalayaWest Bengal721636India School of Computer Science and Engineering Vellore Institute of TechnologyChennai600127Tamil NaduIndia Division of Applied Mathematics Wonkwang UniversityIksan-SiJeonbuk54538Korea School of Computer Science and Engineering Center for Cyber Physical SystemsVellore Institute of TechnologyChennai600127Tamil NaduIndia Department of Instrumentation Engineering PDEAs College of EngineeringManjari412307PuneIndia Engineering and Research Services HCL TechnologiesChennai600119India

Fuzzy sets have undergone several expansions and generalisations in the literature,including Atanasov’s intuitionistic fuzzy sets,type 2 fuzzy sets,and fuzzy multisets,to name a few.They can be regarded as fuzzy multisets from a formal standpoint;nevertheless,their interpretation differs from the two other approaches to fuzzy multisets that are currently available.Hesitating fuzzy sets(HFS)are very useful if consultants have hesitation in dealing with group decision-making problems between several possible memberships.However,these possible memberships can be not only crisp values in[0,1],but also interval values during a practical evaluation process.Hesitant bipolar valued fuzzy set(HBVFS)is a generalization of HFS.This paper aims to introduce a general framework of multi-attribute group decision-making using social network.We propose two types of decision-making processes:Type-1 decision-making process and Type-2 decision-making process.In the Type-1 decision-making process,the experts’original opinion is proces for thefinal ranking of alternatives.In Type-2 decision making processs,there are two major aspects we consider.First,consistency tests and checking of consensus models are given for detecting that the judgments are logically rational.Otherwise,the framework demands(partial)decision-makers to review their assessments.Second,the coherence and consensus of several HBVFSs are established forfinal ranking of alternatives.The proposed framework is clarified by an example of software packages selection of a university.

关键词： Group decision-making aggregation operators hesitant bipolar-valued fuzzy set

Medical Waste Treatment Station Selection Based on Linguistic q-Rung Orthopair Fuzzy Numbers

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Computer Modeling in Engineering & Sciences 2021年第10期129卷 117-148页

作者： Jie Ling Xinmei Li Mingwei Lin College of Mathematics and Informatics Fujian Normal UniversityFuzhou350117China Digital Fujian Internet-of-Things Laboratory of Environmental Monitoring Fujian Normal UniversityFuzhou350117China

During the COVID-19 outbreak,the use of single-use medical supplies increased significantly.It is essential to select suitable sites for establishing medical waste treatment stations.It is a big challenge to solve the medical waste treatment station selection problem due to some conflicting factors.This paper proposes a multi-attribute decision-making(MADM)method based on the partitioned Maclaurin symmetric mean(PMSM)operator.For the medical waste treatment station selection problem,the factors or attributes(these two terms can be interchanged.)in the same clusters are closely related,and the attributes in different clusters have no relationships.The partitioned Maclaurin symmetric mean function(PMSMF)can handle these complex attribute relationships.Hence,we extend the PMSM operator to process the linguistic q-rung orthopair fuzzy numbers(Lq-ROFNs)and propose the linguistic q-rung orthopair fuzzy partitioned Maclaurin symmetric mean(Lq-ROFPMSM)operator and its weighted form(Lq-ROFWPMSM).To reduce the negative impact of unreasonable data on the final output results,we propose the linguistic q-rung orthopair fuzzy partitioned dual Maclaurin symmetric mean(Lq-ROFPDMSM)operator and its weighted form(Lq-ROFWPDMSM).We also discuss the characteristics and typical examples of the above operators.A novel MADM method uses the Lq-ROFWPMSM operator and the Lq-ROFWPDMSM operator to solve the medical waste treatment station selection problem.Finally,the usability and superiority of the proposed method are verified by comparing it with previous methods.

关键词： Medical waste treatment station linguistic q-rung orthopair fuzzy sets aggregation operators partitioned dual maclaurin symmetric mean operators

Multi-Criteria Decision Making Based on Bipolar Picture Fuzzy operators and New Distance Measures

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Computer Modeling in Engineering & Sciences 2021年第5期127卷 771-800页

作者： Muhammad Riaz Harish Garg Hafiz Muhammad Athar Farid Ronnason Chinram Department of Mathematics University of the PunjabLahore54590Pakistan School of Mathematics Thapar Institute of Engineering and Technology(Deemed University)Patiala147004India Algebra and Applications Research Unit Division of Computational ScienceFaculty of SciencePrince of Songkla UniversityHat YaiSongkhla90110Thailand Centre of Excellence in Mathematics Bangkok10400Thailand

This paper aims to introduce the novel concept of the bipolar picture fuzzy set(BPFS)as a hybrid structure of bipolar fuzzy set(BFS)and picture fuzzy set(PFS).BPFS is a new kind of fuzzy sets to deal with bipolarity(both positive and negative aspects)to each membership degree(belonging-ness),neutral membership(not decided),and non-membership degree(refusal).In this article,some basic properties of bipolar picture fuzzy sets(BPFSs)and their fundamental operations are introduced.The score function,accuracy function and certainty function are suggested to discuss the comparability of bipolar picture fuzzy numbers(BPFNs).Additionally,the concept of new distance measures of BPFSs is presented to discuss geometrical properties of BPFSs.In the context of BPFSs,certain aggregation operators(AOs)named as“bipolar picture fuzzy weighted geometric(BPFWG)operator,bipolar picture fuzzy ordered weighted geometric(BPFOWG)operator and bipolar picture fuzzy hybrid geometric(BPFHG)operator”are defined for information aggregation of BPFNs.Based on the proposed AOs,a new multicriteria decision-making(MCDM)approach is proposed to address uncertain real-life situations.Finally,a practical application of proposed methodology is also illustrated to discuss its feasibility and applicability.

关键词： Bipolar picture fuzzy set aggregation operators distance measures pattern recognition MCDM